Discrete Geodesics and Cellular Automata

Abstract : This paper proposes a dynamical notion of discrete geodesics, understood as straightest trajectories in discretized curved spacetime. The notion is generic, as it is formulated in terms of a general deviation function, but readily specializes to metric spaces such as discretized pseudo-riemannian manifolds. It is effective: an algorithm for computing these geodesics naturally follows, which allows numerical validation—as shown by computing the perihelion shift of a Mercury-like planet. It is consistent, in the continuum limit, with the standard notion of timelike geodesics in a pseudo-riemannian manifold. Whether the algorithm fits within the framework of cellular automata is discussed at length.
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Pablo Arrighi, Gilles Dowek. Discrete Geodesics and Cellular Automata. Theory and Practice of Natural Computing, Dec 2015, Mieres, Spain. ⟨10.1007/978-3-319-26841-5_11⟩. ⟨hal-01252131⟩

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